Question

This is one of my homework questions please help me work through it. Thank you!

Answer 1

The formula for calculating the magnitude of a vector a is expressed as

`\text{IaI = }\sqrt[]{(x2-x1)^2+(y2-y1)^2}`

a) For vector u, from the graph,

x1 = - 1, y1 = 2

x2 = 4, y2 = 6

`\begin{gathered} \text{IuI = }\sqrt[]{(6-2)^2+(4--1)^2}\text{ = }\sqrt[]{4^2+(4+1)^2} \\ \text{IuI = }\sqrt[]{16\text{ + 25}} \\ \text{IuI = }\sqrt[]{41} \end{gathered}`

b) For vector v,

x1 = 0, y1 = 0

x2 = 5, y2 = 4

`\begin{gathered} \text{IvI = }\sqrt[]{(4-0)^2+(5-0)^2}\text{ = }\sqrt[]{4^2+5^2} \\ \text{IvI = }\sqrt[]{41} \end{gathered}`

Thus, u = v because they have the same magnitude and direction